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For every set of primitive propositions and agents there is a canonicalKripke structure and a canonical map from any Kripke structure (defined withthe same primitive propositions and agents) to this canonical one. A cell ofthe canonical Kripke structure is a set C such that if any agent considers apoint x in C to be possible then all the other points considered possible bythis agent are also in C. A cell C has finite fanout if at every point in Cevery agent considers possible only finitely many other points. We demonstratea cell of this canonical Kripke structure such that every Kripke structure thatmaps to this cell does so surjectively, yet this cell does not have finitefanout.

The Common Knowledge of Formula Exclusion